{
  "id": "cond-mat/0103246",
  "version": "v2",
  "published": "2001-03-12T10:07:22.000Z",
  "updated": "2001-10-01T17:07:11.000Z",
  "title": "Signatures of Randomness in Quantum Chaos",
  "authors": [
    "Piotr Garbaczewski"
  ],
  "comment": "Major revision, presented at XVI Marian Smoluchowski Symposium on Statistical Physics",
  "journal": "Acta Phys. Pol. B 33, (2002), 1001-1024",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "nlin.CD"
  ],
  "abstract": "We investigate toy dynamical models of energy-level repulsion in quantum eigenvalue sequences. We focus on parametric (with respect to a running coupling or \"complexity\" parameter) stochastic processes that are capable of relaxing towards a stationary regime (e. g. equilibrium, invariant asymptotic measure). In view of ergodic property, that makes them appropriate for the study of short-range fluctuations in any disordered, randomly-looking spectral sequence (as exemplified e. g. by empirical nearest-neighbor spacings histograms of various quantum systems). The pertinent Markov diffusion-type processes (with values in the space of spacings) share a general form of forward drifts $b(x) = {{N-1}\\over {2x}} - x$, where $x>0$ stands for the spacing value. Here $N = 2,3,5$ correspond to the familiar (generic) random-matrix theory inspired cases, based on the exploitation of the Wigner surmise (usually regarded as an approximate formula). N=4 corresponds to the (non-generic) non-Hermitian Ginibre ensemble. The result appears to be exact in the context of $2\\times 2$ random matrices and indicates a potential validity of other non-generic $N>5$ level repulsion laws.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-10-01T17:07:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum chaos",
      "pertinent markov diffusion-type processes",
      "randomness",
      "signatures",
      "empirical nearest-neighbor spacings histograms"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Acta Physica Polonica B",
      "year": 2002,
      "month": "Apr",
      "volume": 33,
      "number": 4,
      "pages": 1001
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002AcPPB..33.1001G"
    }
  }
}